Personally I would like to see asexual repoduction with more focus on the mechanics of the robot. Here's what I'm thinking:
You have a base unit with different attachment points for things like sensors, solar panels, drive motors. You start with a basic robot, 1 solar panel, 2 small motors and some basic ultra sonic and touch sensors. The robot then has to run a small maze which may have a few obsticals in it, like a pit or something. Once it comes back out at the end it will be in a main area were there are some containers with the parts to make another robot. It will then select all the part the remake itself, but will also make one small change, such as change to faster motors or add another solar panel.
Obversly a human operater will have to assembly the new robot. The new robot then runs the maze. If the new design isn't any good it won't make the out of the maze.
I'm not sure how an new design can make an older design extinct, maybe a flipper on the robots and you run two against each other. The move though as small maze each, fight in a central area, then the winner moves to the reproduction area.

Of corse I have no idea how to build such an experment._________________Get Some!!!